I had a 30min ride from work in -10 today and Knog Nomad gloves proved to be nice and toasty, anything colder than that I would have to put some merino liner under for a short ride but my hands would be fine without the liner on a longer ride once they warm up. Gloves are rated from -5 to +8 but being a bit bulky they are a bit problematic when used on a road bike as shifting on STI’s is a problem. MTB, shifting and braking no problem. Not really cheap now as still over £28 on eBay.
If You go the cheap route and buy some snowboarding/ski gloves, take something like a lock on grip or even a small bottle to see how they feel when You hold the grip/bottle. Every cycling glove I had had a longer thumb as when You grip the bars it won’t feel too tight. My normal Berghaus windstopper goves are not as good for riding compared to others due to the cut. Aldi/Lidl cycling stuff is good value for money, always worth a look as they had a winter clothes special day recently.